The 4-vector of the polarization \(a = (0, \, \vec{\xi })\)  of the spin-\(\tfrac{1}{2}\)  particle is defined in its rest frame in which the particle 4-momentum is \(p = (m, \, 0)\) . In this frame the axial vector \(\vec{\xi }\)  is an average of the particle spin, \(\vec{\xi }= \tfrac{2}{\hbar }\langle \, \vec{S} \, \rangle \)   [1]}.
